Trithagorean: Difference between revisions

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+'''Trithagorean''' or '''freivaldthree''' is a [[just intonation]], [[tritave]]-repeating [[nonoctave]] scale invented by [[Jake Freivald]] in 2011. It has 13 unequal tones per tritave.
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:guest|guest]] and made on <tt>2013-03-26 03:32:01 UTC</tt>.<br>
+== Freivald's description ==
-: The original revision id was <tt>417882740</tt>.<br>
+"
-: The revision comment was: <tt></tt><br>
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
+This was an experiment with something I jokingly call "trithagorean" -- a 3/1-repeating scale based on repeated stackings of perfect 5/3s and 9/5s. That can give you an MOS at 13 or 15 notes, but I only used about 10 of them. There are no octaves anywhere in this scale.
-<h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">! trithagorean.scl
+In [[cents]], that's this:
+* 0.000 unison, perfect prime
+* 133.238 large limma, BP small semitone
+* 266.475 two (large limma, BP small semitone)
+* 399.713
+* 617.884
+* 751.121
+* 884.359 major sixth, BP sixth
+* 1017.596 just minor seventh, BP seventh
+* 1150.834 octave - maximal diesis
+* 1284.071
+* 1502.242
+* 1635.480
+* 1768.717 classic augmented eleventh, BP twelfth
+* 1901.955 perfect 12th
+"
+== Scala file ==
+<pre>
+! freivaldthree.scl
 !
-[[Jake Freivald]]'s Trithagorean scale: Can be viewed as ennealimmal with period 3 and generator 5/3; -6 to 6 missing -3 (i.e., 243/125) to fit into 12 tones.
+JI tritave repeating scale, similar to ennon13
+! Mode of the 13-note tritave MOS of ennealimmal
+!
+/25
+/625
+/15625
+/2187
+/81
+/3
+/5
+/125
+/3125
+/6561
+/243
+/9
+/1
+</pre>
+As (3, 5) monzos:
+|3 -2&gt;
+|6 -4&gt;
+|9 -6&gt;
+|5 -7&gt;
+|3 -4&gt;
+|-1 1&gt;
+|2 -1&gt;
+|5 -3&gt;
+|8 -5&gt;
+|-6 8&gt;
+|-5 6&gt;
+|-2 2&gt;
+|1 0&gt;
+=== 12-tone version ===
+<pre>
+! trithagorean.scl
+!
+Jake Freivald's Trithagorean scale: Can be viewed as ennealimmal with period 3 and generator 5/3; -6 to 6 missing -3 (i.e., 243/125) to fit into 12 tones.
 !
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 /243
 /9
-/1</pre></div>
+/1
-<h4>Original HTML content:</h4>
+</pre>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;trithagorean&lt;/title&gt;&lt;/head&gt;&lt;body&gt;! trithagorean.scl&lt;br /&gt;
-!&lt;br /&gt;
+== Music ==
-&lt;a class="wiki_link" href="/Jake%20Freivald"&gt;Jake Freivald&lt;/a&gt;'s Trithagorean scale: Can be viewed as ennealimmal with period 3 and generator 5/3; -6 to 6 missing -3 (i.e., 243/125) to fit into 12 tones.&lt;br /&gt;
+; [[Jake Freivald]]
-&lt;br /&gt;
+* [https://soundcloud.com/jdfreivald/three-days-apart ''Three Days Apart''] (2011)
-!&lt;br /&gt;
-/25&lt;br /&gt;
+[[Category:13-tone scales]]
-/625&lt;br /&gt;
+[[Category:Just intonation scales]]
-/15625&lt;br /&gt;
+[[Category:Tritave]]
-/2187&lt;br /&gt;
+[[Category:MOS scales]]
-/81&lt;br /&gt;
+[[Category:Ennealimmal]]
-/3&lt;br /&gt;
+[[Category:Pages with Scala files]]
-/5&lt;br /&gt;
+[[Category:trithagorean]]
-/3125&lt;br /&gt;
-/6561&lt;br /&gt;
-/243&lt;br /&gt;
-/9&lt;br /&gt;
-/1&lt;/body&gt;&lt;/html&gt;</pre></div>